Koichi Mayumi

Mechanics of slide-ring gels: novel entropic elasticity of a topological network formed by ring and string

Slide-ring (SR) gels are polymer networks with movable cross-links that are prepared by cross-linking polyrotaxane (PR) in which many cyclic molecules are threaded into a linear polymer chain. The elastic modulus E of SR gels shows a unique dependence on cross-linking density: at a high cross-linking density, E decreases with increasing cross-linking density. This tendency is not in agreement with conventional rubber elasticity theory. In order to explain this abnormal dependence, we propose a novel molecular theory for SR gels, which considers the alignment entropy of cyclic molecules on polymer networks. The alignment yields new entropic elasticity of the slidable network in SR gels.

Fracture of dual crosslink gels with permanent and transient crosslinks

We have carried out systematic fracture experiments in a single edge notch geometry over a range of stretch rates on dual crosslink hydrogels made from polyvinyl alcohol chains chemically crosslinked with glutaraldehyde and physically crosslinked with borate ions. If the energy release rate necessary for crack propagation was calculated conventionally, by using the work done to deform the sample to the critical value of stretch c where the crack propagates, we found that the fracture energy  peaks around ~ 0.001 s-1 before decreasing sharply with increasing stretch rate, in contradiction with the measurements of crack velocity. Combining simulations and experimental observations, we propose therefore here a general method to separate the energy dissipated during loading before crack propagation, from that which is dissipated during crack propagation. For fast loading rates (with a characteristic strain rate only slightly lower than the inverse of the typical breaking time of physical bonds), this improved method to estimate a local energy release rate glocal at the onset of crack propagation, gives a value of the local fracture energy  local which is constant, consistent with the constant value of the crack propagation velocity measured experimentally. Using this improved method we also obtain the very interesting result that the dual crosslink gels have a much higher value of fracture energy at low loading rates than at high loading rates, contrary to the situation in classical chemically crosslinked elastic networks.

Rheology of a dual crosslink self-healing gel: Theory and measurement using parallel-plate torsional rheometry

Tough hydrogels can be synthesized by incorporating self-healing physical crosslinks in a chemically crosslinked gel network. Due to the breaking and reattachment of these physical crosslinks, these gels exhibit a rate-dependent behavior that can be different from a classical linear viscoelastic solid. In this work, we develop a theory to describe the linear mechanical response of a dual-crosslink gel in a parallel-plate torsional rheometer. Our theory is based on a newly developed finite strain constitutive model. We show that some of the parameters in the constitutive model can be determined by carrying oscillatory torsional experiments. For consistency, we also show that the torsion data in an oscillatory test can be predicted using our theory with parameters obtained from tension tests. Our theory provides a basis for interpreting and understanding the test data of these gels obtained from rheometry.

Dynamic light-scattering measurement of sieving polymer solutions for protein separation on SDS CE

We evaluated the mesh size and homogeneity of polymer network by dynamic light scattering and discussed the relationship between the physical properties of polymer network and the protein separation behavior by capillary polymer electrophoresis. We compared three kinds of sieving polymers in solutions with a wide range of molecular weights and concentrations: polyacrylamide and polyethylene oxide as flexible polymers, and hydroxyethyl cellulose as a semiflexible polymer. We found that the mobility of protein was dominated primarily by the mesh size ξ, irrespective of the type of sieving polymers, and the peak spacing between protein peaks increased drastically in the range of ξ<10 nm, where the mobility also decreased. And the peak widths were dependent on the molecular species of sieving polymers and their homogeneity of polymer network. We proposed that a polymer network with a homogenous mesh size of less than 10 nm is the best sieving medium for separation of the proteins in the molecular weight range 14 300–97 200 Da from the view point of the resolution in protein separation.

Molecular weight dependency of polyrotaxane-cross-linked polymer gel extensibility

This work investigates the influence of the molecular weight of polyrotaxane (PR) cross-linkers on the extensibility of polymer gels. The polymer gels, which were prepared using PR cross-linkers of three different molecular weights but the same number of cross-linking points per unit volume of gel, have almost the same Youngs modulus. By contrast, the extensibility and rupture strength of the polymer gels are substantially increased with increasing molecular weight of the PR cross-linker.

Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

Synthesis, structure, and mechanical properties of silica nanocomposite polyrotaxane gels

Summary A significantly soft and tough nanocomposite gel was realized by a novel network formed using cyclodextrin-based polyrotaxanes. Covalent bond formation between the cyclic components of polyrotaxanes and the surface of silica nanoparticles (15 nm diameter) resulted in an infinite network structure without direct bonds between the main chain polymer and the silica. Small-angle X-ray scattering revealed that the homogeneous distribution of silica nanoparticles in solution was maintained in the gel state. Such homogeneous nanocomposite gels were obtained with at least 30 wt % silica content, and the Young’s modulus increased with silica content. Gelation did not occur without silica. This suggests that the silica nanoparticles behave as cross-linkers. Viscoelastic measurements of the nanocomposite gels showed no stress relaxation regardless of the silica content for <20% compression strain, indicating an infinite stable network without physical cross-links that have finite lifetime. On the other hand, the infinite network exhibited an abnormally low Young’s modulus, ~1 kPa, which is not explainable by traditional rubber theory. In addition, the composite gels were tough enough to completely maintain the network structure under 80% compression strain. These toughness and softness properties are attributable to both the characteristic sliding of polymer chains through the immobilized cyclodextrins on the silica nanoparticle and the entropic contribution of the cyclic components to the elasticity of the gels.

Buffers to suppress sodium dodecyl sulfate adsorption to polyethylene oxide for protein separation on capillary polymer electrophoresis

Although polyethylene oxide (PEO) offers several advantages as a sieving polymer in SDS capillary polymer electrophoresis (SDS‐CPE), solution properties of PEO cause deterioration in the electrophoresis because PEO in solution aggregates itself, degrades into smaller pieces, and forms polymer–micelle complexes with SDS. We examined protein separation on SDS‐CPE with PEO as a sieving matrix in four individual buffer solutions: Tris‐CHES, Tris‐Gly, Tris‐Tricine, and Tris‐HCl buffers. The solution properties of PEO as a sieving matrix in those buffers were examined by dynamic light scattering (DLS) and by surface tension. Preferential SDS adsorption onto PEO disturbed protein–SDS complexation and impaired the protein separation efficiency. Substantial adsorption of SDS to PEO was particularly observed in Tris‐Gly buffer. The Tris‐CHES buffer prevented SDS from adsorbing onto the PEO. Only Tris‐CHES buffer achieved separation of six proteins. This study demonstrated efficient protein separation on SDS‐CPE with PEO.

Static and dynamic light scattering studies on dilute polyrotaxane solutions

Static and dynamic light scattering measurements were performed for dilute polyrotaxane solutions in different types of solvent systems, i.e. dimethylacetamide (DMAc) or dimethylformamide (DMF) containing 1-6 wt% lithium chloride (LiCl), 1 M aqueous sodium hydroxide (NaOH) and dimethylsulfoxide (DMSO). No aggregation of the polyrotaxane in DMF/LiCl was confirmed in the present study. Radius of gyration of the dissolved polyrotaxane was largest in NaOHaq., followed by values in amide solvents/LiCl and that in DMSO, and was probably dominated not by Coulombic repulsion but by the mutual affinity between solvent and polyrotaxane. Ratio of radius of gyration to hydrodynamic radius suggested the flexible random-coiled conformation in DMSO and relatively more extended, semi-flexible ones in amide solvents/LiCl and NaOHaq. The obtained values of second virial coefficient and weight average molecular weight seemed to be affected by a potential change in differential refractive index increments, caused by selective macrocationization or ionization.

Ductile Glass of Polyrotaxane Toughened by Stretch-Induced Intramolecular Phase Separation

A new class of ductile glasses is created from a thermoplastic polyrotaxane. The hard glass, which has a Youngs modulus of 1 GPa, shows crazing, necking, and strain hardening with a total elongation of 330%. Stress concentration is prevented through a unique stretch-induced intramolecular phase separation of the cyclic components and the exposed backbone. In situ synchrotron X-ray scattering studies indicate that the backbone polymer chains slip through the cyclic components in the regions where the stress is concentrated.